{"id":434,"date":"2026-05-05T04:45:33","date_gmt":"2026-05-05T04:45:33","guid":{"rendered":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-phan-boi-chau-nghe-an\/"},"modified":"2026-05-05T07:18:22","modified_gmt":"2026-05-05T07:18:22","slug":"de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-phan-boi-chau-nghe-an","status":"publish","type":"post","link":"https:\/\/79.buffdemo.com\/index.php\/2026\/05\/05\/de-thi-thu-tot-nghiep-thpt-mon-toan-2024-2025-truong-thpt-chuyen-phan-boi-chau-nghe-an\/","title":{"rendered":"\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT chuy\u00ean Phan B\u1ed9i Ch\u00e2u \u2013 Ngh\u1ec7 An"},"content":{"rendered":"

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/strong> l\u00e0 t\u00e0i li\u1ec7u \u00f4n luy\u1ec7n h\u1eefu \u00edch gi\u00fap h\u1ecdc sinh l\u1edbp 12 l\u00e0m quen v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 thi ch\u00ednh th\u1ee9c v\u00e0 r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng gi\u1ea3i b\u00e0i hi\u1ec7u qu\u1ea3. \u0110\u1ec1 bao ph\u1ee7 \u0111\u1ea7y \u0111\u1ee7 c\u00e1c chuy\u00ean \u0111\u1ec1 tr\u1ecdng t\u00e2m nh\u01b0 h\u00e0m s\u1ed1, t\u00edch ph\u00e2n, h\u00ecnh h\u1ecdc kh\u00f4ng gian, x\u00e1c su\u1ea5t, \u1ee9ng d\u1ee5ng \u0111\u1ea1o h\u00e0m,\u2026 ph\u00f9 h\u1ee3p v\u1edbi xu h\u01b0\u1edbng ra \u0111\u1ec1 m\u1edbi nh\u1ea5t. H\u00e3y c\u00f9ng T\u00e0i Li\u1ec7u \u00d4n Thi<\/a><\/strong> kh\u00e1m ph\u00e1 ngay \u0111\u1ec1 thi n\u00e0y \u0111\u1ec3 luy\u1ec7n t\u1eadp v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng gi\u1ea3i to\u00e1n hi\u1ec7u qu\u1ea3 nh\u1ea5t cho k\u1ef3 thi quan tr\u1ecdng s\u1eafp t\u1edbi nh\u00e9!<\/p>\n

N\u1ed9i dung \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/span><\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/strong>\u00a0c\u00f3 c\u1ea5u tr\u00fac b\u00e1m s\u00e1t \u0111\u1ec1 thi minh h\u1ecda c\u1ee7a B\u1ed9 GD&\u0110T. \u0110\u1ec1 bao g\u1ed3m ba ph\u1ea7n ch\u00ednh tr\u1ea3i \u0111\u1ec1u c\u00e1c d\u1ea1ng b\u00e0i tr\u1ecdng t\u00e2m c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 12 v\u00e0 l\u1ed3ng gh\u00e9p c\u00e1c c\u00e2u h\u1ecfi ph\u00e2n h\u00f3a gi\u00fap \u0111\u00e1nh gi\u00e1 to\u00e0n di\u1ec7n n\u0103ng l\u1ef1c h\u1ecdc sinh. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00e2u h\u1ecfi minh h\u1ecda trong \u0111\u1ec1 thi:<\/p>\n

Ph\u1ea7n I: Tr\u1eafc nghi\u1ec7m nhi\u1ec1u l\u1ef1a ch\u1ecdn (12 c\u00e2u)<\/strong><\/span><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 f(x) li\u00ean t\u1ee5c tr\u00ean mathbbR th\u1ecfa m\u00e3n \\int_0^1 f(x)dx = 2 \\quad \\text{v\u00e0} \\quad \\int_0^3 f(x)dx = 7. Khi \u0111\u00f3 int\u2081\u00b3 f(x)dx b\u1eb1ng<\/p>\n

A. -9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0B. 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 C. -5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 D. 5<\/p>\n

C\u00e2u 2.<\/strong> Trong kh\u00f4ng gian Oxyz , cho m\u1eb7t ph\u1eb3ng (P) \u0111i qua \u0111i\u1ec3m A(1;0;-2) v\u00e0 c\u00f3 m\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (1; -1; 2) . Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng (P) l\u00e0<\/p>\n

A. x \u2013 y \u2013 2z + 3 = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 B. x \u2013 y + 2z \u2013 3 = 0 \u00a0 \u00a0 \u00a0 \u00a0 C. x \u2013 y + 2z + 3 = 0 \u00a0 \u00a0 \u00a0 \u00a0 D. x + y + 2z + 3 = 0<\/p>\n

Ph\u1ea7n II: Tr\u1eafc nghi\u1ec7m \u0111\u00fang\/sai (4 c\u00e2u, m\u1ed7i c\u00e2u 4 \u00fd)<\/strong><\/span><\/p>\n

C\u00e2u 1.<\/strong> Cho h\u00e0m s\u1ed1 y = ax + b + c\/x+d ( a,b,c,d in mathbbR ) c\u00f3 \u0111\u1ed3 th\u1ecb nh\u01b0 h\u00ecnh v\u1ebd sau:<\/p>\n

\"\"<\/p>\n

a) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x = -2 .
\nb) Gi\u00e1 tr\u1ecb b = -4 .
\nc) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00e3 cho c\u00f3 ti\u1ec7m c\u1eadn xi\u00ean l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng y = 2x – 4 .
\nd) H\u00e0m s\u1ed1 \u0111\u00e3 cho l\u00e0 y = -2x -4 – 2\/x+2 .<\/p>\n

C\u00e2u 2.<\/strong> C\u00e2y \u0111\u1eadu H\u00e0 Lan khi tr\u1ed3ng c\u00f3 chi\u1ec1u cao 3 centim\u00e9t. G\u1ecdi h(t) l\u00e0 \u0111\u1ed9 cao t\u00ednh b\u1eb1ng centim\u00e9t c\u1ee7a c\u00e2y \u0111\u1eadu H\u00e0 Lan t\u1ea1i th\u1eddi \u0111i\u1ec3m t k\u1ec3 t\u1eeb khi \u0111\u01b0\u1ee3c tr\u1ed3ng, v\u1edbi t t\u00ednh theo tu\u1ea7n. Kh\u1ea3o s\u00e1t cho th\u1ea5y t\u1ed1c \u0111\u1ed9 t\u0103ng chi\u1ec1u cao c\u1ee7a c\u00e2y \u0111\u1eadu H\u00e0 Lan sau khi tr\u1ed3ng l\u00e0 h'(t) = -0.02t\u00b3 + 0.3t\u00b2 centim\u00e9t\/tu\u1ea7n.<\/p>\n

a) H\u00e0m s\u1ed1 h(t) c\u00f3 c\u00f4ng th\u1ee9c l\u00e0 h(t) = -0,005t\u2074 + 0,1t\u00b3 .
\nb) Giai \u0111o\u1ea1n t\u0103ng tr\u01b0\u1edfng c\u1ee7a c\u00e2y \u0111\u1eadu H\u00e0 Lan \u0111\u00e3 k\u00e9o d\u00e0i 15 tu\u1ea7n.
\nc) Chi\u1ec1u cao t\u1ed1i \u0111a c\u1ee7a c\u00e2y \u0111\u1eadu H\u00e0 Lan \u0111o l\u00e0 88 centim\u00e9t.
\nd) V\u00e0o th\u1eddi \u0111i\u1ec3m c\u00e2y \u0111\u1eadu H\u00e0 Lan ph\u00e1t tri\u1ec3n nhanh nh\u1ea5t th\u00ec chi\u1ec1u cao c\u1ee7a c\u00e2y l\u00e0 53 centim\u00e9t.<\/p>\n

Ph\u1ea7n III: Tr\u1eafc nghi\u1ec7m tr\u1ea3 l\u1eddi ng\u1eafn (6 c\u00e2u)<\/strong><\/span><\/p>\n

C\u00e2u 1.<\/strong> Trong l\u1ea7n \u0111\u1ea7u ti\u00ean nu\u00f4i g\u00e0, m\u1ed9t trang tr\u1ea1i do thi\u1ebfu kinh nghi\u1ec7m n\u00ean d\u1ef1 t\u00ednh l\u01b0\u1ee3ng th\u1ee9c \u0103n cho g\u00e0 h\u1eb1ng ng\u00e0y l\u00e0 kh\u00f4ng \u0111\u1ed5i v\u00e0 \u0111\u00e3 d\u1ef1 tr\u1eef th\u1ee9c \u0103n \u0111\u1ee7 d\u00f9ng trong 50 ng\u00e0y. Nh\u01b0ng th\u1ef1c t\u1ebf, theo s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a g\u00e0, \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o ch\u1ea5t l\u01b0\u1ee3ng th\u00ec k\u1ec3 t\u1eeb ng\u00e0y th\u1ee9 2 tr\u1edf \u0111i l\u01b0\u1ee3ng th\u1ee9c \u0103n nu\u00f4i g\u00e0 m\u1ed7i ng\u00e0y c\u1ee7a trang tr\u1ea1i \u0111\u00e3 t\u0103ng th\u00eam 1\\% so v\u1edbi ng\u00e0y tr\u01b0\u1edbc \u0111\u00f3. H\u1ecfi l\u01b0\u1ee3ng th\u1ee9c \u0103n m\u00e0 trang tr\u1ea1i d\u1ef1 tr\u1eef \u0111\u1ee7 d\u00f9ng cho g\u00e0 \u0103n t\u1ed1i \u0111a bao nhi\u00eau ng\u00e0y m\u00e0 v\u1eabn \u0111\u1ea3m b\u1ea3o ch\u1ea5t l\u01b0\u1ee3ng \u0103n m\u1ed7i ng\u00e0y? (l\u1ea5y k\u1ebft qu\u1ea3 s\u1ed1 ng\u00e0y l\u00e0 s\u1ed1 nguy\u00ean).<\/p>\n

C\u00e2u 2.<\/strong> Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh b\u1eb1ng 3 v\u00e0 c\u1ea1nh b\u00ean SA vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y. Bi\u1ebft g\u00f3c nh\u1ecb di\u1ec7n [B, SC, D] b\u1eb1ng 120^\u00b0 . Th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p S.ABCD b\u1eb1ng bao nhi\u00eau?<\/p>\n

T\u1ea3i \u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An<\/strong><\/h2>\n

\u0110\u1ec1 thi th\u1eed t\u1ed1t nghi\u1ec7p THPT m\u00f4n To\u00e1n 2024 \u2013 2025 tr\u01b0\u1eddng THPT chuy\u00ean Phan B\u1ed9i Ch\u00e2u Ngh\u1ec7 An <\/strong>l\u00e0 t\u00e0i li\u1ec7u \u00f4n t\u1eadp v\u00e0ng d\u00e0nh cho h\u1ecdc sinh 12 chu\u1ea9n b\u1ecb b\u01b0\u1edbc v\u00e0o k\u1ef3 thi quan tr\u1ecdng. B\u1ed9 \u0111\u1ec1 thi th\u1eed THPT qu\u1ed1c gia m\u00f4n to\u00e1n 2025<\/a> \u0111\u01b0\u1ee3c bi\u00ean so\u1ea1n b\u1edfi \u0111\u1ed9i ng\u0169 gi\u00e1o vi\u00ean chuy\u00ean m\u00f4n cao t\u1eeb ng\u00f4i tr\u01b0\u1eddng danh ti\u1ebfng mi\u1ec1n Trung b\u00e1m s\u00e1t c\u1ea5u tr\u00fac ch\u00ednh th\u1ee9c v\u1edbi \u0111a d\u1ea1ng d\u1ea1ng b\u00e0i t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. H\u00e3y nhanh tay t\u1ea3i v\u1ec1 t\u00e0i li\u1ec7u qu\u00fd gi\u00e1 n\u00e0y \u0111\u1ec3 t\u1ef1 tin \u0111\u1ea1t \u0111i\u1ec3m cao trong k\u1ef3 thi s\u1eafp t\u1edbi!<\/p>\n